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anisotropies cannot explain the small (in magnitude) anisotropy in isoprene relative t o cyclopentadiene. According t o the above discussions, we conclude that the anisotropies in the ring molecules listed in Table V from cyclopentadiene t o benzene must be described in terms of both local and nonlocal contributions. From the isoprene-cyclopentadiene study, the local effects and the ring current contribute roughly an equal amount t o the anisotropy. If this is true in general, it lends support t o the modified ring-current theories. 3-5 We are trying to develop a set of local group anisotropies in order t o determine with more confidence the magnitude of the nonlocal effects, but refinements, along with more data, are necessary. For example, in isoprene there is the possibility that the anisotropy might change depending on the location of the methyl group or that the methyl and methylene carbon atoms in isoprene and cyclopentadiene have a different
anisotropy even though both carbon atoms have sp3 hybridization. The first possibility is easy t o test by measuring the anisotropies in cis- and trans-1,3pentadiene. We are presently trying t o do this, but the line strengths are extremely weak. As another example, the anisotropies of acrolein and crotonaldehyde would give the anisotropy of the methyl group. (The anisotropy for acrolein is very close to that for isoprene.39) But at the present time, we feel that these effects will be small (less than 5 units) and will not explain the factor of 2 between the anisotropies of isoprene and cyclopentadiene. Acknowledgment. The support of the National Science Foundation is gratefully acknowledged. We would also like t o thank 3. Musher for some interesting comments on magnetic susceptibilities which stimulated much of the work in the present paper. (39) R. C. Benson and W. H. Flygare, unpublished results.
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Molecular Orbital Calculations on the Phenonium Cation Transformation 2-Phenylethyl Eugene I. Snyder' Contribution f r o m the Department of Chemistry, East Tennessee State University, Johnson City, Tennessee 37601. Received M a y 9, 1970 Abstract: The reaction coordinate for the transformation, classical 2-phenylethyl ~ phenonium cation, has been
mapped using CND0/2 calculations. That the results of such calculations must be quantitatively grossly incorrect was shown by the results of similar calculationsfor the correspondingradical species. We show that CNDO/2 has a built-in bias for three-menibered ring formation, at least for the Pople and Wiberg parametrizations. Extended Hiickel calculations on the same problem give results which are the qualitative inverse of those of CNDO. However, known experimental data demonstrate that the EHT results are also quantitatively incorrect. Thus neither semiempirical calculation gives results which can be trusted.
T
he nature of the 2-phenylethyl cation remains a question of current intereste2 To assist in the structural formulation, we have employed semiempirical molecular orbital calculations to construct the potential energy surface for the equilibrium CsHsCHzCHz+
e +CHzCHzCsHj
When this work was performed, the C N D O SCF MO treatment of Pople3 seemed the best compromise between relevant quantum-mechanical completeness and computational manageability. Using parameters suggested by Wiberg,4 the energy of the 2-phenylethyl cation was calculated as a function of the angle 0.
Results would be most valid for the gas-phase reaction, but remain meaningful for the condensed phase provided that the solvation energy of species along the reaction coordinate does not change significantly. (1) All computational work was performed at the University of Connecticut. The basic program obtained from the Quantum Chemistry Program for Exchange was modified somewhat, including the addition of a subroutine for bond index calculations. Because the prediagonalization feature of the original program sometimes caused errors to mount, resulting in divergence in the SCF-iteration sequence, it was omitted in most calculations. Address correspondence to the author at Kraftco Corp., Research and Development Division, Glenview, Ill. 60025. (2) P. v. R. Schleyer, et al., J . Amer. Chem. SOC.,91, 4291, 4294, 4296, 4297, 7508 (1969); S. Winstein, er al., ibid., 90, 6546 (1968); 91, 4300 (1969); J. L. Coke, et al., ibid., 91, 1154, 4284 (1969); R. J. Jablonski and E. I. Snyder, ibid., 91, 4445 (1969); J. E. Nordlander and W. G. Deadman, ibid., 90, 1590 (1968); G. A. Olah and A. M. White, ibid., 91, 5801 (1969). For a viewpoint significantly different from those expressed above, see S. L. Loukas, M. R. Velkou, and G. A . Gregoriou, Chem. Commun., 251 (1970), and references cited therein.
Snyder
For every value of 0 the geometry of the cation was optimized to minimize the total energy (electronic nuclear repulsive). This optimization procedure was continued uatil all bond distances and angles were within 0.02 A and 2", respectively, of the structure corresponding to the absolute minimum energy geometry. Coordinates of the various nuclei were calculated sub-
+
(3) J. A. Pople and G. A. Segal, J . Chem. Phys., 43, S136 (1965); 4, 3289 (1966). (4) K. B. Wiberg, J . Amer. Chem. SOC.,90, 59 (1968).
MO CaIcuIation on the 2-PhenyIethyl+ Phenonium Cation Transformation
7530 “C
Table 11. Bond Index-Charge Densitv Profiles for Cations
.. I
Atom no.
Figure 1. Angular dependence of the energy of the 2-phenylethyl cation (-) and radical (---) according to EHT (upper two curves) and CNDO (lower two curves) calculations.
ject to several geometric constraints imposed on the molecule. Firstly, the alkyl fragment (atoms 1-6) had a local plane of symmetry passing through C3-Cl-Ci. Secondly, the planar aryl portion, with its local C2\, symmetry and the C2 axis through Ci Clo, was so constructed that bond lengths Ci--Ckr Cb-CY = Cy-C1o, and the angle Cs-Ci-Clr were the only independent parameters. (All aryl C-H bond lengths were assumed equal.) The angles Ca-C9-Clo and CY Cl0-Cl1 were made identical, which forced any change of the C8-Ci-CI2 angle to be reflected mainly in the CiCs--C9angle. Bond angles and distances for structures with the extreme values of 0 employed, and the total energy calculated for those structures, are giien in Table I. Results are graphically displayed in Figure 1. Table I. Optimized Geometrical Parameters for Open (“Classical”) and Cyclic (Phenonium) 2-Phenylethyl Cationsa
C3-C4 C3-Hl C4-Hj C4-Ci
c7-cs C*-Cs, co-CiO Aromatic C-H L Hi-Cz-Hz L Hi-C3-C4 L C&-H; L Hj-CrH8 L c3-crci (E e) L c12-ci-c, L C,-C12-Cn L C12-C11-C,o
E(cation), au
Open
Cyclic
1.42 1.13 1.13 1.54 1.42 1.42 1.12 120 120 113 111 109 120 120 120 - 60.3546
1.47 1.13 1.13 1.57 1.45 1.42 1.12 116 117 1 I7 I16 61.9 116 119.9 122.1 - 60.5448
Bond distances in Bngstroms, angles in degrees.
Bond indices5 and charge densities for these structures and the “n-complex” structure (cide irifra) are listed in Table 11. The results of these calculations may be summarized as follows. (1) The cyclic cation is considerably more stable than the open one (however, cide infra). Furthermore, the potential energy decreases continuously from the open ion to that of CSvsymmetry with no indication of local minima or maxima. This suggests the uselessness of referring to an open or “classical” 2 phenylethyl cation, for it has no significant energy barrier to surmount in its conversion to the cyclic or “nonclassical phenonium” ion, and is thermodynam( 5 ) I
